Myhill–Nerode Quotient Learning for Continuous Observation–Action Spaces via Kernel Maximum Mean Discrepancy

Your manuscript is accepted. This revision fixes the variant (T) sampler mismatch. Theorem 1 and Appendix A now cover the `per_traj` sampler with a correctly derived budget. You also report the more conservative T-pt results candidly and withdraw the claim that no longer holds. The novelty statement now acknowledges Mixed LICORS, and the artifact manifest has immutable commit hashes and a table-to-file map. The P^fix attribution is now supported by 10 seeds and restricted to the cases you tested. Before publication, please fix the cross-references, the leftover placeholder and the Appendix E table map listed in the editorial notes; none of these affects the validity of your claims.

Verdict: accept. All five concerns from the round-2 decision are resolved in the manuscript, and the revision adds no new correctness, validity, novelty or reproducibility problem. (1) Sampler/estimand: resolved. Section 3 (T2) now defines variant (T) with the `per_traj` sampler, whose window law is exactly P_b. `per_bin` is kept only as the labelled ablation (T-pb). Tables 4–5 report P, T-pt and T-pb side by side, and Finding (i) withdraws the earlier 'T matches P' claim. (2) Trajectory bound: resolved. Theorem 1 now requires N ≥ 10m*/π_min. Appendix A derives it from Binomial(N_s, π_b) counts with N_s ≥ N/5, a Chernoff bound and a union bound, with no τ or T terms. The quantile-edge DKW step yields the B² term, which the paper says is not tight. (3) Novelty claim: resolved. The Introduction ('Two-sample testing itself is not new'), Section 2 and the Section 5 discussion acknowledge Mixed LICORS. They restate the distinction as the estimand Q*_B plus an analysed bound. (4) Artifacts: resolved. Appendix E gives the repository, the v1 commit hash 83f9f42…, the new-file commit 2c16829…, the file and script lists, and a table-to-file map. (5) P^fix attribution: resolved. Finding (iii) now reports 10 Dec-Tiger seeds at N=20000 and K-cycle runs at B=2K, and restricts the attribution to the cases tested, excluding Tiger at B=8 and K=8 at B=2n. The remaining defects are cross-referencing and placeholder text, which do not affect the validity of any claim.

Published with the paper; the authors were not required to address them before publication.

• In Section 4 ('Which guarantee applies to which procedure'), replace the leftover placeholder '(RESULT-T-SUMMARY)' and the broken reference '(eq. eq:m-bound' with the intended text and equation number.
• Throughout Sections 1, 4 and 5 and the Limitations, correct inconsistent table and remark cross-references: the (T) results are Tables 4–5 but are cited as Table 3, ARI is cited as Table 2/3, 'Remark 2' is cited for the guarantee scope, and the baselines table is cited as both Table 5 and Table 6.
• In Appendix E, align the table-to-file map with the final table numbering, for example by giving `partition_baselines.csv` for the baselines table instead of the blanket 'Tables 1–8 ← Layer 1–3 files'.
• In Appendix C ('Revision experiments'), add `partition_accuracy_pertraj.csv`, `partition_accuracy_2n.csv`, `T_traj_scaling.csv` and `tiger_T_scaling_pertraj.csv` to the result-file list so that it matches Appendix E.
• In Appendix A, Remark 5, state that the m_max=300 calculation applies to procedure (P) or capped samplers, since the theorem's `per_traj` variant is uncapped.